Many optical materials exhibit different responses to optical waves of different wavelengths. One well-known phenomenon is chromatic dispersion, often simply referred to as "dispersion", in which the index of the refraction of a medium is dependent on the wavelength of an optical wave. Dispersion can cause optical waves of different wavelengths to travel at different speeds in a given medium, since the speed of light is dependent on the index of refraction.
Dispersion of optical materials in general relates nonlinearly to the wavelength. Group velocity is often used to characterize the dispersion. Group velocity is related to the derivative with respect to frequency of the propagation constant of an optical wave in a medium. The first-order group velocity dispersion is typically expressed as a change in light propagation time over a unit length of fiber with respect to a change in light wavelength. For conventional fibers in telecommunication, the first-order group velocity dispersion is on the order of 10 ps/nm/km at 1550 nm.
In many applications, an optical signal is composed of spectral components of different wavelengths. For example, a single-frequency optical carrier may be modulated in order to impose information on the carrier. Such modulation generates modulation sidebands at different frequencies from the carrier frequency. For another example, optical pulses, which are widely used in optical data processing and communication applications, contain spectral components in a certain spectral range. The dispersion effect may cause adverse effects on the signal due to the different delays on the different spectral components.
Dispersion in particular presents obstacles to increasing system data rates and transmission distances without signal repeaters in either single-channel or wavelength-division-multiplexed ("WDM") fiber communication systems. Data transmission rates up to 10 Gbit/s or higher may be needed in order to meet the increasing demand in the marketplace. Dispersion can be accumulated over distance to induce pulse broadening or spread. Two adjacent pulses in a pulse train thus may overlap with each other at a high data rate due to dispersion. Such pulse overlapping can often cause errors in data transmission.
The dispersion effect in fiber systems can be significantly reduced by using an optical carrier of a narrow linewidth at or near a zero-dispersion wavelength of the fiber. For example, fiber systems operating near 1.3 .mu.m with single-mode DFB lasers as light sources may be used for this purpose.
Alternatively, the dispersion may be compensated by using dispersion compensating elements. This can be accomplished by, for example, implementing a dispersion-compensating fiber ("DCF") to introduce dispersion with an opposite sign to the accumulated dispersion in a fiber link. Typically, a DCF may be many times more dispersive than a conventional fiber (e.g., a factor of 5 to 10). One DCF-compensated system is described by Nuyts et al. in "Performance improvement of 10 Gb/s standard fiber transmission systems by using SPM effect in the dispersion compensated fiber," IEEE Photon. Tech. Lett. 8, pp. 1406-1408 (1996).
Another approach to compensating for dispersion uses a fiber grating with linearly chirped grating periods. See, for example, Loh et al., "10 Gb/s transmission over 700 km of standard single-mode fiber with 10-cm chirped fiber grating compensator and duobinary transmitter," IEEE Photon. Tech. Lett. 8, 1258-1260 (1996). A spectral component in an optical signal with a wavelength satisfying a Bragg phase-matching condition is reflected back from the fiber grating. Other spectral components are transmitted through the grating. The Bragg phase-matching conditions at different positions in the fiber grating are differentiated by chirping the grating period.
The resonant wavelength of the fiber grating changes with the position. As the grating period increases or decreases along a direction in the fiber grating, the resonant wavelength increases or decreases accordingly. Therefore, different spectral components in an optical signal are reflected back at different locations and have different delays. Such wavelength-dependent delays can be used to negate the accumulated dispersion in a fiber link.
A fiber grating with a uniform period may also be used to produce different delays in the reflected waves at different locations for compensating the dispersion. Ohn et al. report a use of 21 stretching piezo segments to cause nonuniform stretching in a uniform fiber grating in "Dispersion variable fibre Bragg grating using a piezoelectric stack," Electron. Lett. 32, pp. 2000-2001 (1996). Since segments of the fiber grating can be stretched by different amounts, different delays for different spectral components at different positions in the fiber can be produced to compensate for dispersion.